Part 1: Literature review: electrode materials for intermediate-temperature SOFCs
1.1. Operation principles of solid oxide fuel cells
1.2. Intermediate-temperature SOFCs: basic approaches and technologies
1.3. Solid electrolyte materials
1.3.1. Ionic conductivity
1.3.2. Stability and electronic conductivity
1.3.3. Thermal expansion
1.4. Electrode reaction mechanisms
1.4.1. Cathode processes
1.4.2. Anode reactions
1.4.3. Role of ionic transport in electrode materials
1.4.4. Effects of solid electrolyte surface
1.4.5. Effects of current collection
1.5. Electrode materials for IT SOFCs
1.5.1. Cathodes
1.5.1.1. Manganites
1.5.1.2. Ferrites
1.5.1.3. Cobaltites
1.5.1.4. Nickelates
1.5.1.5. Cuprates
1.5.1.6. Composite materials
1.5.2. Anodes
1.5.2.1. Me-YSZ cermets
1.5.2.2. CeO
2-based materials
1.5.2.3. Alternative anode compositions
1.5.3. Surface modification of solid electrolyte
1.5.4. Modification of electrode layers
1.6. Concluding remarks: promising directions in the developments of novel
electrode materials
2
2
4
6
7
10
12
13
14
25
32
37
39
41
41
41
48
52
56
59
60
64
64
68
69
72
74
76
Part 2: Experimental
2.1. Synthesis and ceramic processing
2.2. X-ray diffraction, chemical analysis, IR absorption spectroscopy and
Mössbauer spectroscopy
2.3. Microstructural studies
2.4. Dilatometry and thermal analysis
2.5. Measurements of the total electrical conductivity and Seebeck coefficient
2.6. Oxygen transport properties
2.6.1. Faradaic efficiency studies
2.6.2. Determination of oxygen permeation fluxes
77
77
80
81
81
82
83
84
86
2.7.2. Cell configuration and measuring set-ups
2.7.3. Selection of glass-ceramic sealants
2.7.4. Electrochemical measurements
2.7.5. Reproducibility tests and assessment of materials interaction
89
89
91
92
Part 3: Cobalt- and nickel-containing phases promising for cathode applications
3.1. General characterization
3.1.1. La
0.3Sr
0.7CoO
3-based perovskites
3.1.2. YBaCo
4O
7+Gand its derivatives
3.1.3. La
2NiO
4-based nickelates
3.2. Oxygen ionic transport
3.2.1. Surface-limited oxygen transport in La
0.3Sr
0.7CoO
3-based solid
solutions
3.2.2. Oxygen ionic conductivity of YBaCo
4O
7+G3.2.3. Oxygen permeability of La
2Ni(M)O
4+G(M = Co, Cu) ceramics
3.3. Role of synthesis method: case studies
3.4. Electrical properties vs. temperature and oxygen partial pressure
3.4.1. Cobalt-containing perovskites
3.4.2. Yttrium-barium cobaltite
3.4.3. K
2NiF
4-type La
2Ni(M)O
4+G(M = Co, Cu)
3.5. Thermal expansion
3.6. Selection of cathode compositions
93
93
93
97
102
106
106
109
112
116
118
118
126
128
133
135
Part 4: Ion-conducting oxide materials as components of cermet anodes
4.1. Zircon-type Ce
1-xA
xVO
4+G(A = Ca, Sr)
4.1.1. Structure, ceramic microstructure and thermal expansion
4.1.2. Oxygen ionic and p-type electronic conduction
4.1.3. Electrical conductivity and Seebeck coefficient vs. p(O
2)
4.1.4. Stability in reducing atmospheres
4.2. Perovskite-type La
0.9Sr
0.1Al
0.85-xMg
0.15Fe
xO
3-G4.2.1. General characterization
4.2.2. Transport properties at atmospheric oxygen pressure
4.2.3. Total conductivity vs. oxygen partial pressure
4.2.4. Partial ionic and electronic conductivities
4.2.5. Thermopower behavior and comments on the hole transport
mechanism
4.3. Fluorite-related TbMO
4-G(M = Zr, Hf)
4.3.1. Structure and microstructure
4.3.2. Thermal expansion
4.3.3. Ionic and electron-hole conductivities under oxidizing conditions
4.3.4. Transport properties in reducing atmospheres
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149
153
154
156
159
163
166
168
168
171
172
175
4.4.3. Transport properties under high p(O
2) gradients
4.4.4. Grain-boundary effects: a case study and selected conclusions
4.5. Partial ionic and electronic conductivities of anode components
188
189
193
Part 5: Processing and electrochemical activity of mixed-conducting electrodes
5.1. SOFC cathode layers in contact with LSGM electrolyte
5.1.1. Fabrication of porous cathode layers
5.1.2. Electrochemical behavior of La
2Ni
0.8Cu
0.2O
4+Gcathodes
5.1.3. YBaCo
4O
7-based electrodes
5.1.4. Critical role of ceramic microstructure and effects of surface
modification
5.1.5. Concluding remarks: factors determining electrochemical activity
5.2. Cellulose-precursor synthesis of SOFC anode components
5.3. Electrochemical performance of cermet anodes
5.3.1. Fabrication and characterization of porous anode layers
5.3.2. Effects of metal/oxide ratio and phase components
5.3.3. Other factors influencing anode performance
5.3.4. Surface modification of cermet layers
5.3.5. Final remarks
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208
213
213
214
218
222
224
Conclusions
225
Future research: selected aspects
230
References
232
Appendixes
Appendix 1: Properties of selected glass-ceramics
Appendix 2: Mössbauer spectroscopy results
Appendix 3: List of publications containing major results of the thesis
257
257
260
263
List of symbols
265
List of abbreviations
269
Index of Materials
271
environmental pollutions presents a serious problem. One family of such devices is the solid oxide fuel cells (SOFCs). Their use is, however, still limited due to economic reasons. Commercialization of the SOFC-based generators requires a considerable decrease in the power-specific production costs, which can be achieved by (i) increasing the cell performance, (ii) further developments of the SOFC production technologies, and (iii) decreasing cost of the construction materials by reducing the operation temperature. These problems can be partly solved by decreasing the cell operation temperature. In the intermediate-temperature (IT) range, the performance of conventional electrode materials is insufficient and the anode and cathode polarization losses become critical, making it necessary to search for the new materials.
The major goal of this work is to elaborate novel electrode materials for the IT SOFC applications, with a special emphasis on the properties important for practical use, including partial electronic and ionic conductivities, oxygen permeability, nonstoichiometry variations, thermal expansion, phase stability and electrode performance. Particular objectives are:
- to prepare a series of layered oxide cobaltite and nickelate materials with perovskite-related or nonperovskite structure, perform their detailed characterization in a wide range of temperatures and oxygen partial pressures and investigate basic trends in the electrochemical behavior of materials most promising for IT SOFC cathode applications;
- to synthesize a series of mixed ionic-electronic conducting oxide phases with fluorite-, pyrochlore-, zircon- and perovskite-related structures, investigate their stability and transport properties under the SOFC operation conditions and test their performance as the anode components;
- to study the influence of synthesis route, microstructure and grain boundary effects on the ionic and electronic transport and electrode properties;
- to elaborate techniques for preparation of submicron oxide powders in order to fabricate porous oxide and cermet electrode layers with homogeneous well-developed microstructure and high electrochemical activity;
- to evaluate the functional roles of oxide and metal components in the IT SOFC anode behavior in order to develop physico- and electrochemical background for cermet optimization;
- to assess major factors determining the IT SOFC cathodes performance and to select the possible strategies for their further improvements.
Part 1: Literature review: electrode materials for intermediate-temperature SOFCs 1.1. Operation principles of solid oxide fuel cells
Solid oxide fuel cells (SOFCs) are electrochemical devices directly converting a chemical energy of fuel oxidation into the electrical energy and heat, using solid oxide as an electrolyte (oxygen anion conductor). The latter serves also as a barrier that prevents mixing of the fuel and oxidant steams. SOFCs operate at elevated temperatures (873 - 1273 K) where significant ionic conduction appears. With respect to the other types of fuel cells, such as alkaline fuel cell (AFC), polymer electrolyte membrane fuel cell (PEMFC), phosphoric acid fuel cell (PAFC) and molten carbonate fuel cell (MCFC), SOFCs attract a great interest due to their high energy-conversion efficiency, fuel flexibility including the prospects to directly operate on natural gas, environmental safety and a possibility to recover exhaust heat [1-9]. A single cell comprises a dense solid electrolyte in contact with porous anode and cathode, onto which a fuel and an oxidant, respectively, are continuously supplied (Fig.1.1).
Anode Cathode Electrolyte O 2-2 e -Fuel Oxidant Load 1/2 O2 H2 H2O 2 e
-Fig.1.1. Schematic representation of H2
-fueled SOFC.
Except for hydrogen, a variety of other fuels, including hydrocarbons (e.g. methane) and carbon monoxide can also be used in SOFCs [1-9]. Electrical current is generated due to the electrochemical reactions at the electrodes, namely, reduction of the oxidant (oxygen from air) at the cathode: - 2-2 1 O +2e O 2 o (1.1)
and oxidation of fuel by the oxygen ions diffused through the electrolyte, at the anode:
2- -2 2 H +O oH O+2e (1.2) 2- -2 CO+O oCO +2e (1.3) 2- -4 2 2
CH +4O o2H O+CO +8e (1.4)
Due to high operating temperatures, the steam reforming and water gas shift reaction may also occur:
4 2 2
CH +H Oo3H +CO (1.5)
2 2 2
producing hydrogen that is easier oxidized at the anode [1,2,5-7,9].
The electrons evolved from the anode are supplied through the external load to the cathode. The open-cirquit cell voltage E0 is determined by the Nernst equation:
cathode 0 2 anode 2 p(O ) RT E ln 4F p(O ) ª º « » ¬ ¼ (1.7) where p(O2) is the oxygen partial pressure at the electrode; R, F, and T are the universal gas
constant, the Faraday constant and the absolute temperature, respectively. The voltage losses in SOFCs are determined by ohmic losses in the cell components and their interfaces, and by the polarization of the electrodes (K):
0
total anode canode
E E IR K K (1.8)
where E is the cell voltage, I is the current through the cell, and Rtotal is the total ohmic resistance. Solid electrolytes should possess maximum ionic conductivity to reduce the ohmic losses and minimum electronic conductivity to reduce the leakage current, over a wide range of the oxygen partial pressures. The anode and the cathode should provide a fast electronic conduction, and also high catalytic activity to fuel oxidation and reduction of molecular O2, respectively. In addition, the materials choice for SOFC technologies is limited for a number of general requirements. All the SOFC components must be compatible in terms of thermal expansion and be thermodynamically stable under cell operation and fabrication conditions. Also, the chemical expansion of the component materials, as well as cation interdiffusion and chemical interactions between them should be minimized or, preferably, absent.
Fig.1.2. Schematic of planar (left) and tubular (right [13]) SOFC designs.
The SOFC operating at 1273 K on the MgO-ZrO2 or Y2O3-ZrO2 electrolyte with Fe3O4 cathode and iron or carbon anode was first proposed by Baur and Preis [2,3,10] in 1937. In 1962 Weissbart and Ruka [2,3,11], at Westinghouse Electric, used Pt-electrodes because of their high conductivity and catalytic activity. Due to a lower cost, later the Ni-based anodes became widely used. Tedmon et al. [2,3,12], at General Electric, applied in 1969 the PrCoO3-G perovskite cathode
showing the high performance but excessively large thermal expansion. A number of other ceramic materials, mostly perovskite-type, were then tested as the cathodes. The common materials used in SOFCs up to now are: yttria-stabilized zirconia as the electrolyte, Sr-doped LaMnO3-G as the cathode and Ni-zirconia cermets as the anode [1-9,13,14].
Two principal cell designs of SOFCs are being developed: planar and tubular, illustrated in Fig.1.2. By the geometrical arrangement, these can be electrolyte-, anode- or cathode- supported, depending on the thickness of the components. In order to achieve commercially feasible productivity, the individual cells are combined into stacks by the electrically-conductive gas-tight interconnectors joining the elements in series or in parallel. Fig.1.3 shows the examples of stack arrangement on the basis of planar and tubular SOFC concepts.
Fig.1.3. The 1.7kW SOFC module (48-cell stack) operating on methane at 1273 K, elaborated by Tokyo Gas
[14] (left), and a stack connected by a nickel felt, elaborated by Siemens Westinghouse [13] (right).
In spite of the advantages with respect to the commercial electric power generation engines, practical application of SOFCs is still limited for the economical reasons, particularly as a result of the high costs of component materials and fabrication methods [1-7].
1.2. Intermediate-temperature SOFCs: basic approaches and technologies
Decreasing operation temperature of SOFCs down to 773 - 973 K, preserving the high performance, is desirable due to important economical and technological advantages. The SOFC-based power plants are commercially viable provided their production costs count less than approximately 0.6-0.8 Euro/W [3-5], while at present this sum is several times higher. Developments of intermediate temperature solid oxide fuel cells (IT SOFCs) are expected to reduce manufacturing costs, in particular by using the low-cost construction materials, such as stainless steels as the interconnects. Another advantage of IT SOFCs is the increase in the mechanical
durability of the stack due to reduced degradation of the cell materials, which may be caused by high operation temperatures and by the thermal cycling, and due to the possibility of using the alternative materials instead of fragile glass-ceramic sealants for the cell hermetic encapsulation. Furthermore, the low operation temperature is favorable for the small, kW-scale SOFC stacks not supposed to be integrated with gas turbines [3,5,15] because this enables to decrease heat losses.
Table 1.1 Comparison of the maximum power densities obtained for planar single cells operating on H2-H2O fuel
Cell type Electrolyte Cathode Anode T, K Power density, W/cm2
Ref.
Anode-supported
YSZ YSZ-La0.85Sr0.15MnO3 Ni-YSZ 1073 0.7 [24]
Anode-supported
YSZ YSZ-La0.8Sr0.2MnO3 Ni-YSZ 923-1073 0.8-1.8 [25]
Anode-supported
YSZ YSZ-La0.8Sr0.2MnO3 Cu-CeO2 1073 0.31 [8]
Anode-supported Ce0.8Gd0.2O2 (CGO) La0.8Sr0.2Fe0.8Co0.2O3 Ni-CGO 773 0.14 [26] Anode-supported Double-layer yttria-doped ceria and zirconia (CYO-YSZ) La0.8Sr0.2Co0.2Fe0.8O3 -CYO composite Ni-YSZ 973-1073 0.47-0.89 [27] Cathode-supported
YSZ with cathode and anode CYO interlayers
La0.85Sr0.15MnO3 Ni-YSZ 973-1073 0.30-0.87 [28] Electrolyte-supported La0.9Sr0.1Ga0.8Mg0.2O3 Sm0.6Sr0.4CoO3 Ni 1073 0.44 [29] Electrolyte-supported La0.9Sr0.1Ga0.8Mg0.2O3 +2 wt % Al2O3 with
cathode and anode Ce0.8Sm0.2O1.9 (CSO)
interlayers
Pr0.6Sr0.4MnO3-CSO
composite
Ni-YSZ 1073 0.245 [30]
Reducing of SOFC operating temperature is associated, however, with increasing role of electrode polarization as a performance-limiting factor, since an apparent activation energy for the polarization resistance is typically higher than that for ionic transport in solid electrolytes [16,17]. Optimization of the cathode and anode compositions and microstructures are, therefore, necessary to achieve sufficiently low overpotentials in the intermediate-temperature range [1,3,16-20]. The ohmic resistance of the electrolytes is also exponentially increasing on cooling (Fig.1.4). In order to keep a sufficiently high level of oxygen ionic transport at reduced temperatures, two approaches can be used: the application of thinner layers of conventional electrolytes, e.g. yttria-stabilized zirconia (YSZ), or the elaboration of alternative electrolyte materials with a higher ionic conduction. The former concept gave rise to the developments of electrode-supported planar intermediate-temperature cells. To produce the electrolyte films, electrode supports and thin
electrode layers, a number of techniques were exploited, for instance, chemical and electrochemical vapor deposition (CVD and ECVD), electrostatic spray deposition (ESD), vacuum plasma spraying (VPS), physical vapor deposition (PVD), laser-deposition, sputtering, electrophoresis, sol-gel method, spray-pyrolysis, screen-printing, tape casting, slurry-coating methods, co-firing, etc. [1-3,21-23]. The majority of these technologies are time- and capital-consuming. Table 1.1 compares the performance of various types of single planar IT SOFCs.
1.3. Solid electrolyte materials
Yttria-stabilized zirconia (YSZ) with cubic fluorite-type structure is one of the most common commercially-produced solid electrolytes. In addition to ZrO2-based materials [31-40], one can list the other well-known solid electrolytes derived from ThO2, HfO2, CeO2 and G-Bi2O3 [5,15,31,32,41-47]. Among the materials with fast oxygen ionic transport, discovered during last 15-17 years, are LaGaO3-based perovskites, doped Bi4V2O11 (BIMEVOX) series, La2Mo2O9-based (LAMOX) phases, Ba2In2O5-derived phases with perovskite- and brownmillerite-like structures, doped Gd2Ti2O7-G pyrochlores and apatite-type Ln10-xB6O26rG (B = Si or Ge) derivatives [30,31,47-57].
Materials deserving no interest for the electrochemical applications due to their specific disadvantages, are not considered below and are only mentioned for the comparison. For example, bismuth oxide-based phases, exhibiting maximum level of oxygen ionic conductivity known to the moment, are however characterized by excessively high lattice expansion on heating, thermodynamic instability under reducing conditions, volatilization of bismuth oxide and extremely high reactivity with the electrode materials, preventing their use as SOFC electrolytes [44]. La2Mo2O9 and LAMOX phases can be regarded as solid electrolytes only under oxidizing conditions below 1000-1100 K, while increasing temperature or decreasing p(O2) results in a substantial n-type electronic conductivity [53]. In addition, these exhibit a high thermal expansion and may degrade under moderately reducing conditions [53]. Ba2In2O5 derivatives may interact with water vapor and CO2, leading to a degradation in performance even under oxidizing conditions [31]. Doped HfO2 and ThO2 materials possess lower oxygen ionic and higher electronic transport in air than their ZrO2- and CeO2-based analogous, and also higher costs [41]. Significant radioactivity of thoria is another serious problem for the practical application.
Designing the electrolyte materials for SOFCs is directed, in general, towards enhancing the stability limits under reducing conditions, increasing the ionic conductivity and suppressing the electronic transport in a wide range of oxygen pressures and temperatures. The oxygen ionic conductivity, the key criterion for the solid electrolytes, is defined by the number of ionic charge carriers and by their mobility. These can be increased using an appropriate doping. For the
materials where the ionic transport occurs via the oxygen vacancy diffusion mechanism, i.e. for most phases mentioned above, probably except for the apatite- and brownmillerite-type materials, acceptor-type doping and/or cation deficiency may increase the oxygen vacancy concentration. Note that this effect is less important for the phases with internal structural disorder, providing a sufficient level of ionic defects; one example is G-Bi2O3. Another factor influencing the ionic transport relates to defect association and ordering processes. When the dopant content becomes excessively high, the positively charged oxygen vacancies may associate with the acceptor cations; that would reduce the effective concentration of mobile ion species. The doping-induced ordering processes in the oxygen sublattice may result even in the phase transitions, e.g. the disordered perovskite may order into the brownmillerite-type structure. Except the concentration of solute cations, their radius plays also an important role in the transport properties and the phase stability. As a rule, the highest ionic conductivity corresponds to materials where the ionic radii of the dopant and cations constituting the host lattice are close. The larger difference in these radii causes the local strains of the lattice, destabilizing the structure and increasing tendencies to ordering and/or phase transformations, as typical for the fluorite-type ZrO2-based solid solutions with rare- and alkaline-earths [33,38,39]. Another comment is that, in many cases, the properties of ion-conducting oxide materials are sensitive to the microstructural phenomena and to the presence of phase impurities. In particular, silica often segregates at the grain boundaries of solid-electrolyte ceramics, dramatically increasing the boundary resistance. Moderate alumina additions may be effective to “clean” the grain boundaries from SiO2 without an essential blocking effect on the transport properties, as observed for YSZ-Al2O3 composites [58,59], whereas higher content of refractory Al2O3 decreases the ionic conductivity [59].
1.3.1. Ionic conductivity
Among the zirconium dioxide polymorphs, the high-temperature cubic fluorite phase shows the highest level of oxygen ionic transport ([33] and references therein). Incorporation of alkaline- and rare-earth elements partially or completely stabilizes this cubic modification to the lower temperatures and creates the oxygen vacancies. Increasing content of the dopant cations above certain level leads to their progressive association with oxygen vacancies and to a decrease in ionic conductivity [33,34,38,39], Fig.1.4A. The highest ionic transport in zirconias corresponds, therefore, to the minimum dopant concentration, sufficient for stabilization of cubic phase [33]. In the ZrO2-Ln2O3 systems, the maximum ionic transport corresponds to the solid solutions with Ln = Yb, Lu, Sc or Y cations [33-37] with the smallest ionic radii, closer to that of Zr4+ [60]. Yb- and Lu-containing compounds are disadvantageous due to their high costs. Zr1-xYxO2-x/2 and Zr1-xScxO 2-x/2 ceramics show the highest ionic conductivity at x = 0.08-0.11 and 0.09-0.11, respectively. In the
ZrO2-MO systems (M = alkaline-earth cation), the cubic fluorite-type solid solutions existing below 1473 K were found only for the Ca-substituted compositions. The maximum conductivity of Zr1-xCaxO2-x ceramics, corresponding to x = 0.13-0.15 [33], is substantially lower than that of Zr 1-xLnxO2-x/2 [33]. In fact, even for the most-conductive materials derived from zirconium dioxide, the level of ionic conductivity allows their application as IT SOFC electrolytes only in the form of films with 10-100 micron-scale thickness.
-5 -4 -3 -2 -1 0
lo
g
V(S
/cm
)
Zr0.92Yb0.08O2-G Zr0.907Sc0.093O2-G Zr 0.92Y0.08O2-G Zr0.50Y0.50O2-G Zr0.92Y0.08O2-G-Al2O3 (90 - 10 wt%)A
lo
g
V(S
/cm
)
-3 -2 -1 0B
Ce 0.9Gd0.1O2-G Ce0.8Gd0.2O 2-G Ce0.8Sm0.2O2-G Ce0.8Y0.2O2-G Ce 0.8Ca0.2O2-G 7 9 11 13 15 -6 -5 -4 -3 -2 -1 010
4/T, K
-1 La0.9Sr0.1AlO3-G La0.9Sr0.1Ga0.8Mg0.2O3-G -Al 2O3 (98-2 wt%) La 0.9Sr0.1Ga0.8Mg0.2O3-G -Al2O3 (95-5 wt%) La 0.9Sr0.1Ga0.8Mg0.2O3-G (La0.9Sr0.1)0.98Ga0.8Mg0.2O 3-G La0.8Sr0.2Ga0.76Mg0.19Co0.05O3-GC
10
4/T, K
-1 7 9 11 13 15 -5 -4 -3 -2 -1 0 Zr0.92Y0.08O2-G Ce 0.8Gd0.2O2-G (La 0.9Sr0.1)0.98Ga0.8Mg0.2O3-G Gd 2Ti2O7 Gd 1.8Ca0.2Ti2O7-G La10Si6O27 La9.75Sr0.25Si6O27-GD
Fig.1.4. Temperature dependencies of the total conductivity of solid electrolytes based on ZrO2 (A, [34-37]),
CeO2-G (B, [5,42,43]), (La,Sr)(Ga,Mg)O3-G (C, [30,49,50]), (La,Sr)AlO3-G (C, [61]) and (La,Sr)10Si6O27 (D,
[56]) and the bulk oxygen ionic conductivity of (Gd,Ca)Ti2O7-G (D, [54]). The data on La0.9Sr0.1Ga0.8Mg0.2O3-G
With respect to the stabilized zirconias, cubic fluorite-type phases based on cerium dioxide possess significantly higher ionic transport dominating under oxidizing conditions (Fig.1.4A-D). In addition, these materials exhibit no phase transitions in air, which makes them attractive for the applications at reduced temperatures. Among the CeO2-G-Ln2O3 and CeO2-G-MO solid solutions, the highest level of oxygen ionic transport is found for Gd- or Sm-doped compositions at x values in Ce1-xLnxO2-G varying from 0.10 to 0.20 [41-43]. Fig.1.4B illustrates selected data on the total conductivity in air. As for the Ce1-xLnxO2-G solid solutions, substitution of cerium with M2+ leads to a higher oxygen ion transport [41]. The solubility of the alkaline-earth cations in Ce-sublattice is, however, quite limited, decreasing on cooling and leading to separation of MCeO3 perovskite-like phases [41].
Another group of materials, promising as solid electrolytes for the IT SOFCs and showing higher ionic conductivity in comparison with stabilized zirconia (Fig.1.4, C and D), are the doped lanthanum gallates with ABO3 perovskite-type structure [48]. Incorporation of lower-valence cations of an appropriate radius into A- and B-sites of LaGaO3 increases the oxygen ionic conductivity. The highest ionic conductivity is achieved when LaGaO3 is doped with strontium rather than calcium or barium [48]. Mg2+, the only bivalent cation with stable oxidation state and ionic radius close to that of Ga3+ [60], can be introduced into the B sublattice [48]. For La1-xSrxGa 1-yMgyO3-G (LSGM) materials, the optimized composition providing maximum ionic transport is found at x = 0.10-0.20 and y = 0.15-0.20. Further increase in M2+ content in the lattice, or introducing of more than 2% A-site substoichiometry, increases the oxygen vacancy concentration, but leads to extensive association processes and/or segregation of secondary phases, thus decreasing ionic transport [48,49]. Contrary to the ceria- and zirconia-based systems [41], minor (<10 mol%) Ga-doping with cations having variable oxidation state, such as cobalt or iron, leads to increasing ionic transport in LSGM ceramics in the low-temperature range [50,51], Fig.1.4C, while the electronic conductivity is still acceptable for the practical use [50].
Despite a relatively low level of ionic conductivity (Fig.1.4D), the materials derived from LnAlO3 perovskites, A10-x(SiO4)6O2rG (A = La, Pr, Nd, Sm, Gd, Dy) apatites and Gd2Ti2O7 pyrochlores are still of interest due to their relatively low costs. One possible application of these ceramics are the protective surface layers at the anode-side of LaGaO3- or CeO2-based electrolytes, exposed to reducing atmospheres or the components of the composite solid electrolytes. In most perovskite and apatite materials, the oxygen ionic conductivity increases with increasing A-site dopant radius. The highest level of ionic transport was achieved for La1-xSrxAlO3-G at x = 0.10 [61], for Gd2-xCaxTi2O7-G at x = 0.20 [54] and for La10-xSrxSi6O27 at x = 0.25 [56] and La9.33+x/3Si6-xAlxO26 series at x = 1.5 [57].
1.3.2. Stability and electronic conductivity
For the Zr1-xScxO2-x/2 systems, partial ordering and/or decomposition of metastable cubic and rhombohedral solid solutions result in relatively fast ageing [33,39]. For instance, the conductivity of 10 mol% Sc-doped zirconia drops by 2 % after exposure in atmospheric air for 83 h at 1273 K and by 7 % at 1123 K [39]. Yttria-stabilized zirconia, characterized by lower costs and higher stability [33,38,39], is considered as more feasible. Zr1-xCaxO2-x/2 fluorite solid solutions even with high Ca-content are still metastable, decomposing below 1123 K into a stable CaZrO3 perovskite and ZrO2 [33]. In air, the p-type electronic conductivity of zirconia-based solid solutions is much lower than that in doped ceria and lanthanum gallate phases. For example, the electronic contribution to the total conductivity of Zr0.9Y0.1O2-G is less than 0.05 % at 1273 K. The oxygen ionic conductivity of yttria-stabilized zirconia is kept predominant down to at least 10-25 at 1173 K [32]. This low-p(O2) boundary of electrolytic domain is quite similar for all ZrO2-Ln2O3 systems. Comparative data on the electronic transport is summarized in Table 1.2.
Table 1.2 Comparison of the parameters of electronic transport in solid electrolyte ceramics, under oxidizing conditions
Composition T, K p(O2), atm te Ve, mS/cm Ref.
Zr0.9Y0.1O2-G 1273 0.21 5.0×10-5 [41] Zr0.9Sc0.1O2-G 1273 0.21 3.8×10 -4 [41] Zr0.85Ca0.15O2-G 1273 0.21 8.6×10 -4 [41] Ce0.8Gd0.2O2-G 873 0.21 6.9×10 -4 0.003 [45] 973 0.21 1.1×10-3 0.015 1123 1.0 3.7×10-3 0.42 [43] La0.9Sr0.1Ga0.8Mg0.2O3-G 1073 0.21 0.36 [52] 1073 10-3 1.0×10-2 [49] (La0.9Sr0.1)0.98Ga0.8Mg0.2O3-G 1073 10 -3 4.7×10-3 [49] Gd1.9Ca0.1Ti2O7-G 1073 1.0 0.11 2.1 [54] La0.9Sr0.1AlO3-G 1073 0.21 0.64 1.9 [61]
Note: te and Ve are the total electronic (p- and n-type) transference number and the total electronic
conductivity, respectively.
Contrary to zirconia, the cubic fluorite-type polymorph of CeO2-G exists in air within all temperature range until the melting point [41]. In air, the level of p-type electronic conductivity in gadolinia-doped ceria is rather low [43,45], Table 1.2. Decreasing oxygen pressure leads, however, to reduction of cerium accompanied with increasing electronic conductivity [41] and significant volume changes, which implies mechanical instability under SOFC operation conditions, i.e. under
the large p(O2) gradients. Increasing the dopant content in (Ce,Ln)O2-G decreases the stability in reducing atmospheres below 1000-1173 K [15,43]. In order to partially suppress these disadvantages, the fuel cell operation temperature should be reduced below 873 K [15]. In particular, 10 mol% Gd-doped ceria is considered as a prospective electrolyte material for the SOFCs operating at 773 K [5,15]. At this low temperature, however, the electrochemical activity of common electrode materials is usually insufficient to provide a high cell performance.
Contrary to zirconia-based solid electrolytes, the conductivity of the doped lanthanum gallate ceramics does not degrade in air [31]. In oxidizing atmospheres, the level of p-type electronic conductivity in LaGaO3-based electrolytes [52] is higher than in gadolinia-doped ceria [43,45], especially at reduced temperatures, e.g. at 973 K the difference becomes one order of magnitude. Nevertheless, the electronic conductivity of LSGM is still minor (Table 1.2) and has no essential effect on the electrolyte performance. The unfavorable factors limiting the applications of Ga-containing ceramics are Ga3+ reduction and gallium oxide volatilization at decreased p(O2), possible segregation of secondary phases during ceramics sintering, and interactions with electrode materials. Choosing appropriate ceramic processing techniques and cell fabrication and exploitation conditions enable to avoid these problems. Under reducing conditions, n-type electronic conductivity of LSGM ceramics is comparable, or even smaller, with respect to stabilized zirconia electrolytes [32,52]. If comparing with ceria-based electrolytes, the doped lanthanum gallates preserve the dominating ionic transport with negligible electronic contribution down to substantially lower oxygen pressures [52], which makes them advantageous for the IT SOFC applications. For example, the low-p(O2) boundary of the electrolytic domain where the contribution of electronic conductivity to the total transport in La0.9Sr0.1Ga0.8Mg0.2O3-G reaches 1 %, corresponds to the oxygen partial pressure of less than 10-30 atm at 1073 K [49], while for Ce0.8Gd0.2O2-G this value is as high as approximately 10-15 atm [44].
The (La,Sr)AlO3-G perovskites and pyrochlore-type (Gd,Ca)2Ti2O7-G possess a substantial p-type electronic conductivity under oxidizing conditions [54,61], Table 1.2, but are significantly more stable to reduction and component volatilization compared to the doped CeO2-G and LaGaO3-G ceramics. In air, the electron transference numbers of Gd1.9Ca0.1Ti2O7-G, 0.07-0.11 at 1073 - 1223 K [54], are close to the maximum level allowable for solid electrolytes. Taking into account the low costs of raw materials, the use of (Gd,Ca)2Ti2O7-G phases for high-temperature applications seems possible. At 873-1173 K, the ionic contribution to total conductivity of La0.9Sr0.1AlO3-G is smaller than 40 % under air/O2 gradient and is t 90 % under 4% H2/air gradient [61]. The performance of lanthanum-strontium aluminates under oxidizing conditions is, thus, relatively poor.
1.3.3. Thermal expansion
Alkaline-earth-doped lanthanum gallates at lower temperatures than 1073 K, Gd2Ti2O7 and stabilized zirconia ceramics exhibit similar and moderate thermal expansion coefficients (TECs), Table 1.3. This is an important advantage of these materials with respect to the (Ce,Ln)O2-G solid solutions, the thermal expansion of which is slightly higher, close to LSGM doped with transition metal cations (Table 1.3). One of the strategies to use ceria-based materials refers to the application of a protective layer of more redox stable electrolyte at the low-p(O2) surface of doped ceria [27]. However, the thermal expansion mismatch may lead to the microcrack formation and mechanical degradation of ceramics on thermal and redox cycling. The long-term operation of such cells seems, therefore, problematic. In addition, possible chemical interactions between the electrolyte materials may result in the formation of highly-resistive interface layers, deteriorating the cell performance [43,62].
Table 1.3 Comparison of the average linear thermal expansion coefficients of solid electrolyte ceramics in air
Composition T, K Du106 , K-1 Ref. Zr0.92Y0.08O2-G 300-1273 10.0 [35] Zr0.92Y0.08O2-G -Al2O3 (90-10 wt%) 300-1273 9.7 [35] Zr0.85Y0.15O2-G 303-1273 10.9 [63] Zr0.5Y0.5O2-G 293-1273 9.4 [33] Ce0.9Gd0.1O2-G 773 12.4 [46] 853 12.5 Ce0.8Gd0.2O2-G 773 12.5 [46] 853 12.6 303-1073 12.5 [63] 303-1273 12.7 La0.9Sr0.1Ga0.8Mg0.2O3-G 303-1073 10.4 [30] 300-1473 11.9 [49] 303-1073 10.9 [63] (La0.9Sr0.1)0.98Ga0.8Mg0.2O3-G 300-1473 11.8 [49] La0.9Sr0.1Ga0.8Mg0.2O3-G -Al2O3 (95-5 wt%) 303-1073 9.9 [30] La0.9Sr0.1Ga0.76Mg0.19Co0.05O3-G 300-1473 12.7 [50] Gd2Ti2O7rG 323-1273 10.8 [55]
The incorporation of Ln2O3 into ceria facilitates Ce4+ reducibility below 1173 K [15] and induces an additional volume expansion on decreasing oxygen pressure. No essential chemical expansion was observed for the LSGM ceramics. For example, the TEC values obtained for
La0.9Sr0.1Ga0.8Mg0.2O3-G in air and in 4% H2 were found equal within the limits of experimental uncertainty [30].
It should be mentioned that small amounts of highly-dispersed Al2O3 may improve sinterability and mechanical properties of YSZ and (La,Sr)(Ga,Mg)O3-G ceramics, particularly due to suppressed grain growth in the course of sintering [30,33,58,59]. These alumina additions to solid electrolyte ceramics enable also to decrease thermal expansion (Table 1.3).
In summary, gadolinia-doped (La,Sr)(Ga,Mg)O3-G and ceria are the most promising electrolyte materials for IT SOFCs, whereas yttria-stabilized zirconia having relatively low ionic conductivity in the intermediate-temperature range can only be used in the film form. The high n-type conductivity of (Ce,Gd)O2-G in reducing atmospheres, resulting in the internal leakage currents, limits their applicability to a great extent. Low-cost (Gd,Ca)2Ti2O7-G can be used, in particular, as a component of the multilayer or composite electrolytes.
1.4. Electrode reaction mechanisms
To design the electrodes with advanced electrochemical properties, a deep knowledge on the mechanisms of electrode reactions is necessary. The electrode reaction consists of a number of serial and/or parallel steps, which can be divided into transport and heterogeneous; in the course of latter, various intermediate electrochemically-active components may be formed. The characteristic steps of the gas electrode reactions include transport in the gas phase to (or from) the gas/electrode or gas/electrolyte interface, adsorption (or desorption) at these surfaces, diffusion to (or from) the reaction zone, and transfer reactions [32,64-70]. The reaction path and the rate-limiting step are dependent of numerous factors, such as the electrode and electrolyte properties and morphology, gas phase composition and pressure, thermal and electrochemical pre-history [32,64-66,69,71]. The electrochemical process is believed to occur in the vicinity (within few microns) of triple-phase boundary (TPB) [32,64,72], the junction of the gas, electronic or mixed conductor (electrode) and ionic conductor (electrolyte), whose length is mostly determined by the electrode microstructure, formed during electrode fabrication. Actual location of the electrochemically active sites depends generally on the volume and surface transport properties of the electrode and electrolyte materials.
On the absence of external current, dynamic equilibrium related to the equal rates of forward and backward reactions, is established at the electrode. The rate of oxygen exchange with the gas phase at the equilibrium electrode potential is reflected by the exchange current, I0 [32]. The I0 quantity characterizes only the steps related to activation polarization, such as adsorption/desorption, chemical reaction or charge-transfer reaction [32]. The limiting current, Ilim, corresponding to the maximum gradient of electrochemically active component concentration, can be realized for transport processes as well as for adsorption or chemical reaction steps [32]. When
the current I is passed or drawn through the cell, the electrode potential M deviates from the equilibrium value M0. This deviation is characterized by the quantity of overpotential K = M - M0
. At microstructural level, the reasons for electrode polarization include local changes in the concentration of electrochemically active components. The electrode polarization resistance defined as: d R dI K K (1.9) in the case of small polarization and a linear I-K dependence [32,64,65], is interrelated with the
exchange or limiting current
0 RT R nF I K or lim RT R nF I K (1.10)
where n is a number depending on the rate-determining step(s). The most widely used tool for the investigations of electrode kinetics is based on the electrochemical impedance spectroscopy and current interruption methods. The problems which may hamper the proper understanding of the electrode kinetics are analyzed in [73].
concentration polarisation ohmic polarisation activation polarisation Theoretical voltage U, V i, A/cm2 Tafel equation: K = a + b ln i i0
exchange current density
K
, V
log i (A/cm2)
Fig.1.5. Examples of current density dependencies of fuel cell voltage (left) and electrode overpotential
(right).
1.4.1. Cathode processes
The overall cathode reaction of oxygen reduction is expressed by Eq.(1.1). Historically the electrode reactions were first studied on the metal electrodes in contact with solid electrolyte (usually YSZ), which are still considered as appropriate model systems for analysis of processes at the gas electrodes [32,64-68,70-72,74-76]. However, even for these relatively simple systems, the electrode reaction mechanisms are complex and their models are still ambiguous. First of all, the
reaction zone expands from TPB over the electrolyte or electrode surfaces [32,64,69,74]. As all solid electrolytes possess some electronic conduction (see Chapter 1.3.2), the electrochemically active sites may be located at the gas/electrolyte interface with electronic charge carriers delivered along the electrolyte surface. In addition, high cathodic overpotentials or currents may result in a partial reduction of the electrolyte surface and increasing electronic transport, favoring the oxygen exchange with electrolyte [64]. In the case of electrodes where oxygen may dissolve in the bulk or form surface compounds, oxygen reduction may directly take place at the electrode/electrolyte interface, as was clearly shown for the O2,Ag | YSZ [32,74]. For mixed ionic-electronic conducting oxide phases used as the SOFC cathodes, the reaction zone may also spread into the gas/electrode interface with the subsequent transfer of reduced oxygen species to the electrolyte along the electrode surface and/or through the electrode bulk. Also, in some cases, another triple-phase boundary of gas/mixed conductor/current collector, should be taken into account [76]. Thus, despite the numerous experimental and theoretical investigations (see, for example, [32,64-89]) of various-type cathodes, identification of the exact reaction mechanism and rate-determining step(s), remains one of the most difficult but the most important tasks. A variety of simplified steps of the cathode reaction and the formulae for particular cases of polarization processes are summarized below, with emphasis on the porous oxide cathodes with mixed oxygen ionic and electronic conductivity.
General equations for diffusion processes
The diffusion processes are generally described by Fick’s first and second laws [90]:
i i i i i i i i c D d ln a j D c RT d ln c § · P ¨ ¸ © ¹ (1.11)
i i i c D c t w w (1.12)
where ji is the flux density, ci is the concentration, ai is the activity, Di is the diffusion coefficient and Pi is the chemical potential of diffusing i-species, and t is the time. The last part of Eq.(1.11) is written taking into account Wagner’s law. The reaction rate-determining diffusion of molecular oxygen in the gas phase (including pores in the electrode layer) appears at reduced oxygen partial pressures and is characterized by the limiting current and reciprocal polarization resistance, both proportional to p(O2) [64,79]. The gas phase can be treated as an ideal binary mixture of O2 and a diluent gas B [77]. Taking into account the diffusion and convection processes at moderate total gas pressure, and assuming an absence of homogeneous gas-phase reactions, one can write [79]:
2 2 2 2 O O B O O j D c c v and 2 2 2 2 O 2 O B O O c D c v c t w w (1.13)
where 2
O B
D is the gas-phase binary (O2-B) diffusion coefficient, v is the molar gas velocity. Gas-phase diffusion can be expressed by Eqs.(1.13) at large pore diameters compared to the mean free path of the gas molecules; the transport in the small pores is described by the Knudsen diffusion [91], taking into account the interaction with pore walls. The bulk diffusion should be considered along with the Knudsen effects; then, considering tortuous path through the porous media, the effective oxygen diffusion coefficient,
2 eff O D ,is given by [25,79,91]: 2 2 2 2 2 K O B O eff O K g O B O D D P D D D W (1.14) where 2 K O
D is the Knudsen diffusion coefficient of oxygen, Wg is the gas-phase tortuosity, P is the porosity. As the diffusion coefficient of molecular oxygen in pores is at least 6 orders of magnitude greater than that of oxygen ions in solids [69], usually the O2 diffusion is not rate-determining for the air electrode until approaching a limiting current. For example, in case of La0.6Sr0.4Fe0.8Co0.2O3-G in contact with Ce0.9Gd0.1O2-G electrolyte, possible gas-phase diffusion polarization was indicated by changing the shape of electrode impedance spectra at p(O2) below ~0.1 atm. [79]. The gas-diffusion limitations for the O2,Pt | YSZ cathode were discarded down to 10-3 atm [67,68].
Oxygen transport through the solid electrolyte bulk occurs under the gradients of both chemical and electrical (M) potentials, typically via vacancy migration [77,79]. Using Eq.(1.11) and Ohm’s law, the current density i is found as:
V V i 2F V I (1.15) where VV is the conductivity and IV = PV + zFMV is the electrochemical potential of oxygen
vacancies in the electrolyte bulk. It should be noted that vacancy redistribution at the electrode/electrolyte interface may lead to the non-linear potential distribution in the electrolyte bulk [64,78]. The role of nonuniform current and potential distribution in the electrolyte using a two-dimensional model was evaluated in the theoretical work [84]. Polarization caused by the ohmic potential drop in the solid electrolyte as function of the cathode microstructure was also discussed in Ref.[78]. As a rule, the ohmic losses, comprised by the IR term in Eq.(1.8), can be separated from the electrode polarization.
The oxygen ion and electron transport through the bulk of a mixed conductor obeys Wagner’s law, stating the interrelated fluxes of ionic and electronic charge carriers. Under the absence of external electrical current, the oxygen flux through a dense mixed conductor, placed in the oxygen chemical potential gradient, is given by [83,90,92]:
2 2 2 1 ion e O 2 O ion e 1 j d 16F L P P V V P V V
³
(1.16)where P1 and P2 are the oxygen electrochemical potentials at the gas/mixed conductor permeate and feed interfaces, Vion and Ve are the partial ionic and electronic conductivities and L is the average length of the migration path. In the framework of the porous electrode theory, Eq.(1.16) is re-written taking into account the porosity and the solid-phase tortuosity; examples of the alternative expressions for the transport through solid mixed-conductor in a porous layer can be found in [77,79].
General equations for interfacial processes
Molecular oxygen from the gas phase may be chemisorbed at the surface of noble-metal electrodes to form ad-atoms [64,65], which is expressed by
2 ad
1
O (gas) s O
2 R (1.17)
where s is an active site at the surface. Oxygen adsorption at the oxide electrode or electrolyte surfaces may occur via various mechanisms and may be conjugated with the charge-transfer reaction(s) [66]. Numerous forms of adsorbed oxygen species are assumed in literature, in particular O2, O, O2-, O22-, O- or O2-. The adsorption isotherm, in the simplest case representing reaction Eq.(1.17) at relatively low surface coverage, obeys the Henry equation [64,93]:
1 2
ad 2
[O ] K p(O ) (1.18)
where K is the adsorption equilibrium constant related to the interatomic adsorbent-adsorbate interaction.
The oxygen pressure dependence of the polarization resistance of Pt electrodes is characterized by a minimum [32,64], attributed to the Pt oxidation and/or to the adsorption kinetics determined by the Langmuir isotherm [64]. The latter assumes a homogeneous adsorbent surface and a uniform adsorption enthalpy distribution along this surface, independent of the presence of adsorbates which are considered non-interacting. The Langmuir isotherm is given for dissociative adsorption Eq.(1.17) by [64,93,94]: 1 2 ad 2 O 1 2 ad max 2 [O ] K p(O ) [O ] 1 K p(O ) T { (1.19) where T is the relative surface coverage and [Oad]max is the maximum concentration of ad-atoms,
corresponding to the completely packed monolayer of adsorbed oxygen species, or the total number of sites available for adsorption. For real systems, the adsorption enthalpy decreases (in absolute value) with surface covering [64,93]; therefore, the applicability of Eq.(1.19) needs often a careful analysis and, in general, Eq.(1.19) should be written in an integral form [64].
For the case of substantially non-uniform adsorbent surface, the Temkin isotherm equation is simplified, at moderate coverage, to [64]:
1 2 ad ad max 0 2 0 RT [O ] [O ] lnª«E p(O ) º» ¬ ¼ D (1.20)
where D0 and E0 are the parameter characterizing the extent of inhomogeneity and the adsorption coefficient at the sites with maximum adsorption enthalpy, respectively. Similar approximation was suggested in [93] for a binary gas adsorption. The oxygen adsorption/desorption process on O2,Pt | YSZ electrode was modeled in [68] as occurring via the formation of intermediate chemisorbed oxygen molecule with subsequent dissociation or desorption.
The information about the actual mechanisms of oxygen adsorption, dissociation and reduction at the solid oxide surface is, in fact, still scarce. Based on the ratio of the oxygen self-diffusion coefficients and the surface exchange coefficients, it was concluded [69,79] that, for optimized cathode microstructures with grain diameter of about 1 Pm and TPB length per unit area greater than 104 cm-1, the oxygen reduction should be governed by an interfacial oxygen exchange process unless the surface transport of oxygen ions to the TPB is rate-determining. The flux density of oxygen chemisorption-dissociation can be expressed by a kinetic equation [64]:
2 2
0 2
O O O
j j T1 (1.21)
where j0O2 is the exchange flux density of oxygen dissociative adsorption. For the limiting oxygen adsorption, the current density is generally defined in [76, 94] by:
2 2
1 2 O,st 1 O,st
i 4Fª«k p(O ) 1 T kc T º»
¬ ¼ (1.22)
where k1 and k1' are the constants of forward and backward processes Eq.(1.17) and TO,st is the steady-state coverage. The situation, when adsorption of molecular oxygen is retarding with the subsequent dissociation of adsorbed O2-s being in the virtual equilibrium, was considered in [95] postulating:
2
a 2 O O i 4F k p(O ) 1 T T (1.23a)
2 2 2 O 1 O O Kd O T T T T (1.23b)
where ka and Kd are the oxygen adsorption and equilibrium dissociation constants, respectively. This process can also be considered as dissociation of the oxygen molecule in the gas phase in immediate proximity to the solid surface, followed by the adsorption of the oxygen atoms [96].
The case of limiting charge-transfer electrochemical reactions should be considered using the Butler-Volmer equation [32,64,67,85,90]:
0 nF nF i i exp exp RT RT ª §D K· §E K·º ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.24)
Electrolyte e -Mixed conductor Gas phase O2 O -O -O 2-O 2-O 2-e -e -O 2-O
-where n is the number of electrons participating in the rate-determining step, D and E are the charge transfer coefficients, i and i0 are the electrical current and exchange current densities, respectively. Eq.(1.24) is linearized to the ohmic electrode polarization at low overpotentials |K| and shows a Tafel-like behavior at large |K| [66]. The equation:
0 F F d i i exp exp C RT RT dt ª §D K· §E K·º K ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.25)
where C is the capacitance of the interface, was used in [79] to describe interfacial charge-transfer reactions with a single activated rate-limiting step. K is stated to be proportional to the difference in the electrochemical potential of the transported species (vacancy, electron, etc.) across the interface.
Two typical combinations of adsorption/charge transfer/diffusion steps are shown in Fig.1.6. It is quite clear that even for the simple electrode systems, there are a great number of paths, spatially expanding the reaction zone. In addition, the possibility of parallel interfacial processes to occur cannot be a priori discarded. When the electrode polarization is determined by several limiting steps, it is very difficult or impossible to isolate them without precisely controlled morphology and composition of the interfaces; the latter situation is, however, far from experimental realization. Electrolyte e -Mixed conductor Gas phase O2 O O O 2-O 2-O 2-e -e -O 2-O
Fig.1.6. Examples of electrochemical reaction pathway for a porous mixed-conducting oxygen electrode,
showing surface diffusion of O ad-atoms (left) and O- sub-ions (right).
Selected models for one and several limiting steps
One version of the possible steps sequence for oxygen reduction at the surface of mixed-conducting oxide cathode (MC) was proposed as [79]:
2 2 O (g)sRh<(O s)- (1.26a) 2 (O s)- sRh<2(O s)- (1.26b) O (O s)- V<<Rh<s (1.26c)
where (O2-s)- and (O-s)- are the adsorbed oxygen O2- and O- sub-ions, respectively. In order to describe these processes, the authors [79] proposed an equation similar to that obtained for charge-transfer reactions, irrespective of the limiting step:
b f 0 s s r r exp exp RT RT ª §D · §D ·º 'I 'I ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.27)
where r is the rate of the limiting step, r0 is the so-called exchange neutral flux density, Df and Db are constants depending on the specific reaction mechanism, and
2 O gas MC MC s O V h 1 2 2 'I I I I is the electrochemical potential difference between the reactants and the products.
For the case of two or more concurrent limiting steps, one possible approach can be based on the example of O2, Pt | YSZ electrode, where electrochemically active component is not soluble. Such an electrode was considered [32,66] as a tightly contacted with electrolyte discontinuously long metallic stripe of a fixed width. The relative roles of the interfacial diffusion rate of oxygen ad-atoms chemisorbed at the metallic electrode and the surface exchange rate were analyzed in Ref.[66]. In the case of the rate-limiting diffusion along the electrode/electrolyte interface which depends, in turn, on the rate of charge-transfer reaction, the current density was expressed by the Butler-Volmer-form equation [66]:
12 0 0 i 2eDc 3F F i exp exp 2RT 2RT l ª § K· § K ·º ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.28a) or
1 1 2 0 0 0 F 3F F
i exp exp exp
2e c 2RT 2RT 2RT i 2eDc l l ª § K ·º ª § K· § K ·º « ¨ ¸» « ¨ ¸ ¨ ¸» J « © ¹» ¬ © ¹ © ¹¼ ¬ ¼ (1.28b) where l is the stripe half-width, c0 is the equilibrium concentration of oxygen adatoms, D is their interfacial diffusion coefficient and J is a constant. Eqs.(1.28a) and (1.28b) are obtained for different boundary conditions.
For the competing charge-transfer, surface diffusion and dissociative adsorption, another equation was derived [68]:
0 3(1 )F 3 F i i A exp exp 7RT 4RT ª § E K· § E K·º « ¨ ¸ ¨ ¸» © ¹ © ¹ ¬ ¼ (1.29)
where A is the electrochemically-active area near the TPB, was simulated; the latter two steps are assumed parallel. The effect of surface coverage on these processes were also discussed ([68] and cited references).
The models for a limiting step involving conjugated processes of interfacial diffusion/migration and heterogeneous exchange, was also discussed in Ref.[32]. For the
dissociative adsorption of oxygen coupled with diffusion along the gas/metal interface (GM), the electrical current per unit TPB length is found as [32]:
1 2 GM 1 1 0 6F 2F i i exp 3exp 2 RT RT ª § K · § K · º ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.30)
Provided the constant oxygen ion concentration at the electrolyte surface, the current corresponding to the diffusion along the metal/electrolyte interface (ME) conjoined with the oxygen transfer to (or from) the electrolyte can be expressed as [32]:
ME 2 2 0 O (1 )F F i i exp exp RT RT ª § D K · T §E K ·º ¨ ¸ ¨ ¸ « » © ¹ © ¹ ¬ ¼ (1.31)
where T is the ratio of the oxygen atom concentration at the GM to the equilibrium concentration. These overpotantial-current dependencies were obtained assuming that: (i) the widths of gas/metal and gas/electrolyte interfaces are much smaller than the corresponding penetration depths of the surface diffusion, (ii) the oxygen diffusion coefficient in the adsorption layer is concentration-independent, and (iii) the adsorption isotherm obeys the Henry equation. Dependence of the total overpotential on current was obtained from Eqs.(1.30) and (1.31), both expressing the interrelated exchange process and the interface diffusion; in this case, however, only numerical solution is possible [32]. Nevertheless, it was concluded [32] that decreasing p(O2) leads to the dominating limitations by Eq.(1.30), while the reaction rate becomes determined by Eq.(1.31) on increasing p(O2). The other processes illustrated in Fig.1.6, except for the oxygen transport through the electrode bulk, can be described by the analogous current-overpotential equations involving relative concentrations of O- subions or electron-holes instead of TO [32].
One important comment should be made for the case when two processes are rate-determining, whatever the reaction path. In such situation, one cannot principally determine characteristics of the separate steps from the results of polarization measurements only. Note also that the processes reflected by Eqs.(1.30) or (1.31) have a mixed character combining the activation and concentration polarization effects. The ratio of diffusion- and exchange-related contributions should change with the electrode depth [32]. As a result, the oxygen activity at the electrode surface may change by several orders of magnitude, decreasing for the cathode and increasing for the anode polarization. Such p(O2) variations may cause irreversible changes in the microstructure and properties of the electrodes.
Similar phenomena, including the adsorbate transport along the electrode/electrolyte interface may take place for the porous perovskite-type oxide cathodes [85]; for metallic electrodes such a reaction pathway was analyzed using two-dimentional model [84]. The effect of cathodic polarization or current on the microstructure and morphology of the (La0.8Sr0.2)1-xMnO3-G (x =
0-0.05) porous layers in contact with 3 mol% Y2O3 - ZrO2 electrolyte were attributed to the formation and migration of oxygen vacancies and manganese ions on the electrode surface [86].
For a mixed-conductor electrode, competitive bulk and surface oxygen transport was discussed in numerous works, e.g. [64,72,79,81-85,87,97,98]. Both these processes and their relative roles depend on the oxygen ion conductivity of the cathode material under given conditions, as discussed below. In turn, the conductivity of the cathode layer (V) should be influenced by the equilibrium with gas environment and by the local overpotential caused by deviations of oxygen activity from the equilibrium values. The reaction mechanism including charge transfer, oxygen adsorption and O2- diffusion through the electrode bulk, was discussed in Ref.[64], assuming that these two effects can be isolated and taking into account the boundary conditions at the mixed conductor/metallic current collector contact. In the case of the overpotential-independent total conductivity, for the adsorption regime the current through the unit triple-phase boundary is interrelated with overpotantial as [64]:
1 2 0 0 0 2F 2F i 2RT Sj exp 1 RT RT ª V § § K · K ·º « ¨ ¨ ¸ ¸» © ¹ © ¹ ¬ ¼ (1.32) where S is the effective electrode surface area on which the electrochemical reaction takes place,
and j0 is the exchange flux density. The adsorption becomes rate-limiting when the oxygen activity in the gas phase is reduced due to high cathodic polarization. For the retarding oxygen ion diffusion through the electrode bulk
1 1 1 2 2 m 0 0 i 2 2F 2F 2FD p(O ) i exp 1 d RT RT § · ª § K · K º ¨ ¸ « ¨ ¸ » ¨ ¸ ¬ © ¹ ¼ © ¹ (1.33) where Di is the effective p(O2)-independent diffusion coefficient, d is the effective thickness of the
diffusion layer, and the m parameter is determined by the oxygen ion formation mechanism in the mixed conductor under equilibrium conditions. When the electrochemical reaction -
2-O2e RO is the rate-limiting step, the current taken from the unit triple-phase boundary is [64]:
1 2 0 0 0 2RTi S F F i exp exp F RT RT ª º V K K § · § · § · ¨ ¸ « ¨ ¸ ¨ ¸» © ¹ ¬ © ¹ © ¹¼ (1.34)
In the extreme cases of high polarization conditions, Eqs.(1.30)-(1.34) present Tafel-like dependencies. Under the low polarization when |2FK/RT| << 1:
1 1 2 2 0 m 0 0 i 2 2F 1 1 d i S RT i 2Fj 2FD p(O ) § · § · K V¨ ¸ ¨ ¸ © ¹ © ¹ (1.35)
where the resistances of all three steps: charge transfer, oxygen adsorption and O2- diffusion through the electrode bulk in series, were taken into account [32,64]. Note that in Eqs.(1.30)-(1.35)
the effective width of the layer where the electrochemical reaction occurs, is assumed much smaller than the electrode thickness.
Table 1.4 The p(O2) exponent (m) for the polarization resistance experimentally obtained for
various cathodes in contact with zirconia or ceria* based electrolytes
Cathode Microstructure T, K p(O2), atm - m Ref.
Pt porous film or mesh 833-983 <10-2 1/2 [64] point 1115 >10-3 1/2 [65] point 1115 <10-4 2/3 [65] Pt-YSZ porous 1273 10-2 - 1 9/10 [74] Pd - - - 1/2 [32] Ag point 966-1139 >10-6 1/2 [65] Au point 1211 >10-3 1/2 [65] 1211 <10-3 1/4 point 1233 10-5 - 1 1/2 [87] La1-xSrxMnO3 (x=0.1-0.4)
point, after high cathodic polarization
1233 10-5 - 1 3/8 [87]
(La0.82Sr0.18)0.82MnO3 porous 1123-1273 10
-2 - 0.21 0.45 - 0.86 (R2) [107] La0.85Sr0.15MnO3 porous 1073-1170 10-3 - 1 1/4 (R2), 1 (R3) [108] La0.8Sr0.2MnO3 porous 1073-1273 <10-3 1 [109] porous 1073-1273 10-3 - 1 1/2 [109] La0.8Sr0.2MnO3 porous 823-1073 10 -3 - 1 1/6 [110] La1-xSrxMnO3 (x=0.3-0.7) porous 1073 10-2-0.5 3/4 [88]
La0.63Sr0.27MnO3 dense 973-1173 10-3 - 1 negative [83]
La0.81Sr0.09MnO3 dense 1073 10-3 - 1 0 [94] SrMnO3 porous 1073 10-2-0.5 1/2 [88] La0.6Ca0.4MnO3 porous >1173 <10 -3 1 [106] porous 973-1173 10-3 - 1 1/2 [106]
La0.6Ca0.4MnO3 porous 1073 6u10-4 - 1 1/3 [111]
La1-xSrxCoO3 (x=0-0.7) porous 873-1073 10-2-0.5 1/4 [88] La0.6Sr0.4CoO3 dense 1073 10 -4 - 1 1/2* [94] Sm0.5Sr0.5CoO3 dense 1073 10-4 - 1 1/2* [113] La1-xSrxCoO3 (x=0.2-0.4) porous 1023 10-2 - 1 0.2 - 0.4* [112] La1-xSrxFeO3 (x=0.3-0.7) porous 1073 10-2 - 0.5 3/4 [88]
La0.6Sr0.4FeO3 porous 1073 2u10-4 - 1 0.17 [111]
La1.9Sr0.1CuO4 porous 1073 10 -3 - 1 0.08 [111] La0.7Sr0.3CrO3 porous 1073 10 -2 - 0.5 1/2 [88]
In the case when the overpotential affects the electronic conductivity of electrode layer, the oxygen pressure dependence can be assumed to vary as 0 1
e e p(O )2 Q
V V , where 0 e
V is the electronic conductivity at unit p(O2). If the oxygen delivery to the reaction zone is limiting, the overpotential and oxygen pressure are interrelated by the Nernst law [64]. Then the overpotential dependence of conductivity is 0 e nF A exp RT K § · V ¨ ¸ Q © ¹, where A 0
is the equilibrium electronic conductivity of the mixed conductor. The general current-voltage relation along the TPB is expressed as [64]:
12 1 1 0 2 0 0 2 1 2 1 2 1 2 exp (a 2b) exp (a 2b) a a i A A (a 2b)(a 2b) a 2b a 2b ª K K º « » ¬ ¼ (1.36) where b nF RT Q ; 0 0 4FSj A A , 1 2F a b
RT and a2 for the adsorption regime; b
1 m i 2 0 8FD p(O ) S A A d , a1 and b 2 2F a b RT
for the regime of limiting ion transport;
2 2 0 8FD(O )p(O )S A A d , 1 4F a b
RT and a2 for the regime of limiting transport of molecular b oxygen. The sign of the b coefficient in Eq.(1.36) coincides with that of 1/Q parameter, where positive or negative value corresponds to the p- or n-type electron transport, respectively. Often, these equations may be simplified yielding the Tafel-type polarization curves or the limiting currents, associated with reduced electronic conductivity of the electrode material under polarization [64]. In Ref.[96], the electronic conductivity was described as a function of electric potential on the mixed conductor, oxygen partial pressures and overpotentials at the cathode and anode.
The reaction mechanism represented by:
2 ad O (g)R2O (1.37a) ad ad O eRO (1.37b) ad TPB O RO (1.37c) 2 TPB O TPB O eV<<RO (1.37d) and two additional pathways with Oad
formation through O2,ad
at the electrode surface or at the TPB were considered in Ref.[89] for the La0.85Sr0.15MnO3-G cathode. In all cases, the oxygen adsorbates were assumed diffusing along the electrode surface. The models were suggested for a single rate-determining step and for two serial processes governing the electrode kinetics, with
other steps being in virtual equilibrium [89]. In particular, when the steps Eq.(1.37b) and (1.37c) are rate-determining, the following equation was obtained:
1
0,2 0,3 0,2 0,3
2F F F
i i i exp 1 i exp i exp
RT RT 2RT ª § K· º ª § K· § K ·º « ¨ ¸ » « ¨ ¸ ¨ ¸» © ¹ © ¹ © ¹ ¬ ¼ ¬ ¼ (1.38)
where i0,2 and i0,3 are the exchange current densities of the steps Eq.(1.37b) and (1.37c), proportional for low surface coverage to p(O2)3/8 and p(O2)1/4, respectively [89].
One of the classical methods of investigating the electrode reaction kinetics is the electrochemical impedance spectroscopy (EIS). Analysis of the electrode response with appropriate equivalent circuits reflecting the model electrochemical process, was performed, for example, in Refs.[64,67,68,77,79,87,99,100]. In this respect, the works [101,102], suggesting a general theoretical framework to study the multi-step reaction mechanisms in aqueous systems, are also worth noting. Contrary to the simple model systems with precisely determined microstructures, ascribing exact physical meaning to the equivalent circuit elements, which represent the process at the porous mixed-conducting electrode, appears quite ambiguous. This leads to difficulties in determining the oxygen reduction kinetics. The literature data on oxygen partial pressure dependencies of the total electrode polarization resistance (Table 1.4) and exchange (or limiting) current is also, in many cases, inconsistent. For the anodes based on metallic nickel, the situation seems even more complex [103,104,105].
1.4.2. Anode reactions
The general relationships for transport and charge-transfer processes, given in Chapter 1.4.1, become more complex in the case of the anode reactions where at least two components in the gas phase should be accounted. Again, as for the investigations of the cathode process, the model anode systems are widely studied, in particular metallic Pt and Ni with a high electrocatalytic activity [114]. Nonetheless, the results are relevant for the practical applications as most common anode compositions are based on Ni-YSZ cermets. The majority of these studies are focused on the oxidation of H2, for the sake of simplicity. There are, however, two other important reasons for the attention to H2-containing fuels. For most anode materials, the electrochemical activity for H2 oxidation is higher compared to CO and CH4, The performance of SOFCs fueled by hydrocarbon conversion products, is primarily dependent on the content of H2 and H2O in the fuel gases. Also, the use of H2-fueled SOFCs is associated with zero emission of green house gases.
The high operation temperatures and catalytic activity of the anode materials enable internal reforming of methane in addition to the electrochemical oxidation, as noted in Chapter 1.1. The reactions Eqs.(1.5) and (1.6) are characterized by the standard enthalpies 'H0
298 of 206 and -41 kJ/mol, respectively. Although the former may be partially compensated by the exothermic
